Question

If f(x) = \(\begin{vmatrix}sec⁡ x & cos ⁡x & sec^2⁡ x + cot ⁡x\, cosec x \\cos^2 ⁡x & cos^2 ⁡x & cosec^2 x \\1 & cos^2 ⁡x & cos^2 ⁡x \end {vmatrix}\) then what is the value of 0∫^π/2 f(x) dx = (π/4 + 8/15)?

(a) (π/4 + 8/15)

(b) (π/4 – 8/15)

(c) (π/4 + 8/15)

(d) (-π/4 + 8/15)

I had been asked this question in unit test.

The query is from Application of Determinants topic in chapter Determinants of Mathematics – Class 12

Answer 1

Right choice is (c) (π/4 + 8/15)

The explanation is: (dy/dx) = (dx/dy)^-1

So, d^2y/dx^2 = -(dx/dy)^-2 d/dx(dx/dy)   

                     = -(dy/dx)^2(d^2x/dy^2)(dy/dx)

                     = d^2y/dx^2 + (dy/dx)^3 d^2y/dx^2 = 0